A Leap-on-Success Exhaustive Search Method to Find Optimal Robust Minimum Redundancy Arrays (RMRAs): New Array Configurations for Sensor Counts 11 to 20

Abstract

Two-fold redundant sparse arrays (TFRAs) are designed to maintain accurate direction estimation even in the event of a single sensor failure, leveraging the deliberate coarray redundancy infused into their design. Robust Minimum Redundancy Arrays (RMRAs), a specialized class of TFRAs, optimize this redundancy to achieve the maximum possible aperture for a given number of sensors. However, finding optimal RMRA configurations is an NP-hard problem, with prior research reporting optimal solutions only for arrays of up to ten sensors. This paper presents newly discovered optimal RMRA configurations for array sizes 11 to 15, identified using a novel Leap-on-Success exhaustive search algorithm that efficiently reduces computational effort by terminating the search upon locating optimal solutions. The robustness of these arrays was validated under all single-element failure scenarios using MATLAB simulations, confirming their superior resilience compared to some existing TFRAs vulnerable to failures at specific sensor positions. Furthermore, near-optimal configurations for array sizes 16 to 20 are also reported, highlighting the potential applicability of the proposed method for larger array designs given sufficient computational resources. This work not only advances the state-of-the-art in RMRA design but also introduces an effective search methodology that can be leveraged for future explorations in array configuration optimization.